Exercise 5 In this exercise, we will develop a model that analyzes the choice of exchange regime based in a political environment where there are two parties, the right and the left, each with distinct preferences regarding public spending and inflation. Both parties are making an effort either to reach or maintain power. Consider a small, open economy with flexible prices and free capital mobility. The economy is populated by two distinct groups of individuals.

The first group is formed by a continuum of consumers, denoted by set IC, and the second composed by politicians, denoted by IP. Individuals from the political group are the only Chapter 11 • Political Economy of Exchange Rate Policy 327 ones who can run for government office. The political group is divided into two subgroups

(parties): the right and the left.

The agents in group IC are both consumers and voters. There is only one consumption good, tradable, that is used as numeraire. Each individual receives a real, exogenous income endowment y . 0 in each period and pays a share τAð0; 1Þ of this income in the form of taxes to the government. In period t 5 2, besides the receipts and expenses for period t 5 1, the agent observes the amount of public goods provided by the government, measured in per capita terms, denoted by g.

Assume that purchasing power parity is valid and that the level of international prices is normalized to 1.

The initial wealth of each agent consists of a real stock, that is, measured in units of domestic goods, of international bonds, f0, and of a nominal stock of money, M0. For each period, the individuals choose how much to consume and how much to allocate of their wealth in international bonds, that pay the holder the return of 1 1 r, or in domestic currency. The real stock of international bonds in period t is denoted by ft, and the nominal stock of domestic currency by Mt. The nominal domestic interest rate is given by it 5 r 1 πt, where r is the international interest rate and πt 5 Pt 2 Pt21 Pt21 is domestic inflation.

Individual iAIC has preferences represented by the following utility function:

Uiðc1; c2; m0; m1; gÞ 5 vðc1Þ 1 ε

ε 2 1

 m

ε21

ε

0 1 β vðc2Þ 1 ε

ε 2 1

 m

ε21

ε

1 1 αiuðgÞ

h i;

where ct represents the consumption of goods in period t, vð:Þ is an increasing and strictly concave function, i.e., v0 . 0 and vv , 0. m1  Mt Pt is the real stock of money in period t, εAð0; 1Þ is a preference parameter in relation to currency, β is the intertemporal discount rate that we assume is equal to the interest rate, β 5 1 1 1 r

, αi is a parameter that captures preference of consumer iAIC in relation to public spending, and uð:Þ is an increasing and concave function.

a. Write the budget constraint for individual jAIC for each period, as well as their intertemporal budget constraint. Interpret these equations.

b. Characterize the solution to the intertemporal optimization problem for this individual.

What conclusion can you make based on the relationships found?

The group of politicians in this economy is divided into two political parties, the right and the left, denoted by IP 5 fR; Lg. The preferences of both parties in this economy can be represented by the following function:

Uiðc1; c2; m0; m1; gÞ 5 vðc1Þ 1 ε

ε 2 1

 m

ε21

ε

0 1 β vðc2Þ 1 ε

ε 2 1

 m

ε21

ε

1 1 αjuðgÞ

h i;

where the symbols and parameters are analogous to those for the individuals who are purely consumers. What differs between the parties are their preferences in relation to public spending, measured by parameter αj. Nevertheless, it is common knowledge that

αR , αL, which means that individuals from the left assign a higher value to government spending than individuals from the right.

328 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS The government in period t 5 1 has a real stock of foreign debt, denoted by b0 and a money supply denoted by M0, in nominal terms. To pay for public spending in the first period, the government issues debt, denoted by b1, and issues money, represented by mt, in real terms, in addition to seigniorage and the collection of taxes, τy, as sources of income. In the second period, the only sources of income are the collection of taxes and seigniorage. In t 5 2, government spending equals g. Assume that the government objective, independent of party, is to maximize the utility of the group each party represents, subject to the budget constraint of each period.

c. Obtain the government budget constraint for each period, along with its intertemporal resource constraint. Interpret your results.

d. Present the aggregate resource constraint for this economy. Based on the results obtained in the item, find the individual consumption for each period.

Assume the government in period t 5 1 chooses the exchange rate regime. Consider that when the government decides to adopt the fixed exchange rate regime, it fixes inflation for period 1 at zero, i.e., π1 5 0, and when it chooses a floating exchange rate regime, it fixes the money supply growth rate at zero, i.e., θ  M1 2 M0 M0 5 0. In a simplified way, begin with the principle that individual preferences of group IC can be represented by the preferences of a median voter, whose preference in relation to government spending is represented by αM. Also assume that the following relation is true:

αR , αM , αL. The timing of events is as follows:

• At the beginning of period 1, the government announces the chosen exchange rate regime.

• In period 1, the median voter makes their choice of c1 and m0.

• The election is at the end of period 1.

• The elected government for period 2 announces the provision of public good (g) at the beginning of the period.

• The median voter chooses c2 and m1.

• The government pays all its debts.

e. Considering that the government in period 1 knows it will not win the elections, what exchange regime will be chosen in period 1? (Tip: You can solve the optimum regime choice using backward induction, that is, first solve the problem faced by the period 2 government and then solve the period 1 government problem, taking into consideration the optimum answer of the government for t 5 2. Also consider possible changes in government, that is, that the period 1 government could be from the right, which will change to one from the left, or the contrary. Also assume that

αM

αR $ 1 1 1 1 1=r

ð Þ 1=ε 2 1

).

f. Now consider that the period 1 government, be it either from the left or the right, knows it will remain in power. With this in mind, what will be the chosen exchange rate regime for period 1? (Tip: You can solve the optimum regime choice problem using backward induction, as was done in the previous item. Use the same hypotheses as in the previous item, if necessary.)